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| United States Patent |
6,051,946
|
|
Yamada
, et al.
|
April 18, 2000
|
Electrical angle detection apparatus, method of detecting electrical
angle, and motor control apparatus
Abstract
The conventional technique can not detect the electrical angle of a
synchronous motor in a sensor-less manner when a high torque is required
under the condition of a low-speed operation of the motor. The direction
that passes through the axis of rotation of the motor and causes a
magnetic flux to pass through a permanent magnet is defined as a d axis,
whereas the direction that is electrically perpendicular to the d axis in
the plane of rotation of the motor is defined as a q axis. In the case
where the motor is required to output a high torque, the technique of the
present invention applies a predetermined detection voltage to the q axis
and determines the electrical angle based on the ratio of electric
currents flowing through the d axis and the q axis. Application of a
negative voltage to the q axis relieves magnetic saturation occurring on
the q axis under a high torque condition and thereby allows detection of
the electrical angle. When a positive voltage is applied to the q axis, on
the other hand, the technique of the present invention refers to a table
which is stored in advance to represent the one-to-one mapping of the
electrical angle to the electric current flowing through the q axis, and
thereby determines the electrical angle.
| Inventors:
|
Yamada; Eiji (Owariasahi, JP);
Kawabata; Yasutomo (Aichi-ken, JP)
|
| Assignee:
|
Toyota Jidosha Kabushiki Kaisha (Toyota, JP)
|
| Appl. No.:
|
151349 |
| Filed:
|
September 10, 1998 |
Foreign Application Priority Data
| Sep 12, 1997[JP] | 9-968096 |
| Nov 20, 1997[JP] | 9-337966 |
| Current U.S. Class: |
318/432; 318/700; 318/720 |
| Intern'l Class: |
H02P 007/00 |
| Field of Search: |
318/254,720,721,138,432,807-811
|
References Cited
U.S. Patent Documents
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| |
| 5028852 | Jul., 1991 | Dunfield | 318/254.
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| |
| 5296794 | Mar., 1994 | Lang, et al.
| |
| 5339012 | Aug., 1994 | Schroedl, et al.
| |
| 5561355 | Oct., 1996 | Ideguchi, et al.
| |
| 5569995 | Oct., 1996 | Kusaka, et al.
| |
| 5608300 | Mar., 1997 | Kawabata et al. | 318/721.
|
| 5648705 | Jul., 1997 | Sitar, et al.
| |
| 5714857 | Feb., 1998 | Mannel, et al.
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| 5726549 | Mar., 1998 | Okuno, et al.
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| 5764020 | Jun., 1998 | Maiocchi.
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| 5783917 | Jul., 1998 | Takekawa.
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| 5793167 | Aug., 1998 | Liang, et al.
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| 5796194 | Aug., 1998 | Archer, et al.
| |
| 5854548 | Dec., 1998 | Taga et al. | 318/721.
|
| 5864217 | Jan., 1999 | Lyons, et al.
| |
| 5903128 | May., 1999 | Sakakibara et al. | 318/721.
|
| 5903129 | May., 1999 | Okuno, et al.
| |
| 5907225 | May., 1999 | Kim.
| |
| 5920161 | Jul., 1999 | Obara et al. | 318/139.
|
| 5952810 | Sep., 1999 | Yamada, et al.
| |
| 5955860 | Sep., 1999 | Taga, et al.
| |
Primary Examiner: Ro; Bentsu
Assistant Examiner: Leykin; Rita
Attorney, Agent or Firm: Oblon, Spivak, McClelland, Maier & Neustadt, P.C.
Claims
What is claimed is:
1. In a synchronous motor that rotates a rotor through an interaction
between a magnetic field occurring when multi-phase alternating currents
are flown through windings and a magnetic field produced by permanent
magnets, an electrical angle detection apparatus that detects an
electrical angle, the electrical angle defining a d-axis direction, which
passes through a center of rotation of said rotor and goes along the
magnetic field produced by said permanent magnets, and a q-axis direction,
which is electrically perpendicular to said d-axis direction in a plane of
rotation of said rotor, said electrical angle detection apparatus
comprising:
a torque voltage controller that applies a torque voltage to said windings,
said torque voltage being applied corresponding to a torque command value
to be output by said synchronous motor;
a detection voltage controller that applies a predetermined detection
voltage in a first direction for a predetermined application time period
to be superposed upon said torque voltage, when said torque command value
is present within a predetermined range, which includes a specific torque
command value that causes magnetic saturation of said windings by
application of said torque voltage;
an electric current detection unit that detects variations in electric
currents flowing in a second direction, which is estimated as said d-axis
direction, and said first direction, which is estimated as said q-axis
direction, corresponding to said superposed detection voltage; and
an electrical angle computation unit that calculates the electrical angle
of said synchronous motor, based on the variations in electric currents
detected by said electric current detection sensor.
2. An electrical angle detection apparatus in accordance with claim 1,
wherein said predetermined detection voltage is a predetermined negative
detection voltage.
3. An electrical angle detection apparatus in accordance with claim 2,
wherein said detection voltage controller applies said predetermined
detection voltage to be superposed upon said torque voltage, only when
said torque command value is not less than a specific value relating to
occurrence of the magnetic saturation.
4. An electrical angle detection apparatus in accordance with claim 2,
wherein at least one of an absolute value of said predetermined detection
voltage applied by said detection voltage controller and said
predetermined application time period monotonously decreases with a
decrease of said torque command value.
5. An electrical angle detection apparatus in accordance with claim 2,
wherein said detection voltage controller applies said predetermined
negative detection voltage in said first direction for a predetermined
first time period to be superposed upon said torque voltage, and
subsequently applies a predetermined positive detection voltage in said
first direction, for a predetermined second time period to be superposed
upon said torque voltage.
6. An electrical angle detection apparatus in accordance with claim 1, said
electrical angle detection apparatus further comprising:
a memory, in which a specific relation of an angular error between an
estimated electrical angle and a true electrical angle to the variation in
electric current flowing in said first direction is stored in advance
against said torque command value,
wherein said electrical angle computation unit reads the angular error
corresponding to the detected variation in electric current from said
specific relation stored in said memory, and thereby calculates the
electrical angle of said synchronous motor.
7. An electrical angle detection apparatus in accordance with claim 6,
wherein said predetermined detection voltage is a predetermined positive
detection voltage.
8. An electrical angle detection apparatus in accordance with claim 6,
wherein said detection voltage controller applies said predetermined
detection voltage to be superposed upon said torque voltage, only when
said torque command value is not less than a specific value relating to
occurrence of the magnetic saturation.
9. In a synchronous motor that rotates a rotor through an interaction
between a magnetic field occurring when multi-phase alternating currents
are flown through windings and a magnetic field produced by permanent
magnets, a method of detecting an electrical angle, the electrical angle
defining a d-axis direction, which passes through a center of rotation of
said rotor and goes along the magnetic field produced by said permanent
magnets, and a q-axis direction, which is electrically perpendicular to
said d-axis direction in a plane of rotation of said rotor, said method
comprising the steps of:
(a) applying a torque voltage to said windings, said torque voltage being
applied corresponding to a torque command value to be output by said
synchronous motor;
(b) applying a predetermined detection voltage in a first direction, which
is estimated as said q-axis direction, for a predetermined application
time period to be superposed upon said torque voltage, when said torque
command value to be output by said synchronous motor is present within a
predetermined range, which includes a specific torque command value that
causes magnetic saturation of said windings by application of said torque
voltage;
(c) detecting variations in electric currents flowing in a second
direction, which is estimated as said d-axis direction, and said first
direction corresponding to said superposed detection voltage; and
(d) calculating the electrical angle of said synchronous motor, based on
the variations in electric currents detected in said step (c).
10. A method in accordance with claim 9, wherein said predetermined
detection voltage is a predetermined negative detection voltage.
11. A method in accordance with claim 9, wherein said step (d) comprises
the step of:
reading an angular error between an estimated electrical angle and a true
electrical angle corresponding to the detected variation in electric
current from a pre-stored relation of the angular error to the variation
in electric current flowing in said first direction and thereby
calculating the electrical angle of said synchronous motor.
12. A motor control apparatus that controls a synchronous motor based on an
electrical angle, said synchronous motor rotating a rotor through an
interaction between a magnetic field occurring when multi-phase
alternating currents are flown through windings and a magnetic field
produced by permanent magnets, the electrical angle defining a d-axis
direction, which passes through a center of rotation of said rotor and
goes along the magnetic field produced by said permanent magnets, and a
q-axis direction, which is electrically perpendicular to said d-axis
direction in a plane of rotation of said rotor, said motor control
apparatus comprising:
a unit that inputs a torque command value to be output by said synchronous
motor;
a torque voltage controller that estimates the electrical angle and applies
a torque voltage, which is set according to the estimated electrical angle
and the input torque command value;
a detection voltage controller that applies a predetermined detection
voltage in a first direction, which is estimated as said q-axis direction,
for a predetermined application time period to be superposed upon said
torque voltage, when said torque command value to be output by said
synchronous motor is present within a predetermined range, which includes
a specific torque command value that causes magnetic saturation of said
windings by application of said torque voltage;
an electric current detection sensor that detects variations in electric
currents flowing in a second direction, which is estimated as said d-axis
direction, and said first direction corresponding to said superposed
detection voltage;
an electrical angle computation unit that calculates the electrical angle
of said synchronous motor, based on the variations in electric currents
detected by said electric current detection sensor; and
a unit that supplies the calculated electrical angle as data used for
estimation of the electrical angle to said voltage controller that
repeatedly applies said superposed voltage.
13. A motor control apparatus in accordance with claim 12, wherein said
predetermined detection voltage is a predetermined negative detection
voltage.
14. A motor control apparatus in accordance with claim 12, said motor
control apparatus further comprising:
a memory, in which a specific relation of an angular error between the
estimated electrical angle and a true electrical angle to the variation in
electric current flowing in said first direction is stored in advance
against said torque command value,
wherein said electrical angle computation unit reads the angular error
corresponding to the detected variation in electric current from said
specific relation stored in said memory, and thereby calculates the
electrical angle of said synchronous motor.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a technique of detecting an electrical
angle of a synchronous motor in a sensor-less manner as well as a
technique of controlling the synchronous motor. More specifically the
present invention pertains to these techniques when the synchronous motor
is either at a stop or at a low-speed rotation.
2. Description of the Related Art
In a synchronous motor that rotates a rotor through an interaction between
a magnetic field occurring when multi-phase alternating currents are flown
through windings and a magnetic field produced by permanent magnets, in
order to obtain a desired rotational torque, it is required to control the
multi-phase alternating currents according to the electrical angle or the
electrical position of the rotor. The electrical angle may be detected
with a sensor, such as a Hall element. It is, however, desirable to detect
the electrical angle in a sensor-less manner, with the view to assuring
the reliability of a control apparatus of the synchronous motor.
There is a known method that detects the electrical angle in a sensor-less
manner when the synchronous motor is either at a stop or a low-speed
rotation. This known method takes advantage of the phenomenon that the
magnetic resistance in a magnetic circuit varies with a variation in angle
of the rotor and changes the inductances of the windings in a salient-pole
permanent magnets-type motor.
The following description regards a permanent magnets-type three-phase
synchronous motor. The synchronous motor is expressed by an equivalent
circuit that has three-phase coils of U, V, and W phases and a permanent
magnet rotating about an axis of rotation as shown in FIG. 4. In the
equivalent circuit, the axis that passes through the N pole of the
permanent magnet as the positive direction is defined as a d axis, whereas
the axis that is electrically perpendicular to the d axis is defined as a
q axis. The magnetic field in the q-axis direction is a main dominant
factor of the torque of the motor. The electrical angle is defined as a
rotational angle .theta. of the axis passing through the U-phase coil and
the d axis. Ld denotes an inductance of the windings when a voltage is
applied to cause a magnetic field in the d-axis direction, and Lq denotes
an inductance of the windings when a voltage is applied to cause a
magnetic field in the q-axis direction. A motor control apparatus, which
controls operation of the synchronous motor, can not first detect the
position of the rotor accurately. The motor control apparatus accordingly
estimates an electrical angle .theta.c, which causes an angular error
.DELTA..theta. deviated from the true electrical angle .theta. as shown in
FIG. 4. The axes estimated as the d axis and the q axis based on the
electrical angle .theta.c by the motor control apparatus are respectively
referred to as a .gamma. axis and a .delta. axis.
In order to detect the electrical angle in this state, the motor control
apparatus applies a voltage in the .gamma.-axis direction and detects
electric currents flowing in the .gamma.-axis direction and in the
.delta.-axis direction corresponding to the applied voltage. In the case
where the .gamma. axis estimated by the motor control apparatus coincides
with the d axis, no electric current is detected in the .delta.-axis
direction. When there is an angular error .DELTA..theta. of the electrical
angle, on the other hand, an electric current is detected in the
.delta.-axis direction. The electric currents in the .gamma.-axis
direction and in the .delta.-axis direction vary with a variation in
angular error .DELTA..theta.. This accordingly enables calculation of the
angular error .DELTA..theta. based on the observed electric currents and
detection of the electrical angle .theta.. The method of calculating the
angular error .DELTA..theta. will be discussed later.
This known method enables the electrical angle to be detected with a
relatively high accuracy when the synchronous motor is either at a stop or
a low-speed rotation. In the synchronous motor under such driving
conditions, however, this method is not applicable to detect the
electrical angle when the torque command value increases to or above the
rated torque of the motor. The studies on the technique of controlling the
motor in a sensor-less manner have only recently started and not yet
referred to this problem.
One possible countermeasure designs the motor to have a sufficiently
marginal rating relative to the required torque. This arrangement,
however, causes another problem of increasing the size and the weight of
the motor.
SUMMARY OF THE INVENTION
The object of the present invention is thus to provide a technique that
detects the electrical angle of a synchronous motor with a high accuracy
and appropriately controls the synchronous motor even when output of a
high torque is required while the synchronous motor is either at a stop or
at a low-speed rotation.
In order to realize the above and the other related objects, the technique
of the present invention applies a predetermined detection voltage in a
direction estimated as a q-axis direction for a predetermined time period
to be superposed upon a torque voltage, when a torque command value is
present within a predetermined range that includes a specific torque
command value, which causes magnetic saturation of windings by application
of the torque voltage. The technique of the invention calculates the
electrical angle of the synchronous motor based on variations in electric
currents flowing through the windings corresponding to the superposed
detection voltage. The torque voltage is applied to the windings
corresponding to a torque command value to be output by the synchronous
motor.
The conventional technique of detecting the electrical angle applies a
predetermined positive voltage in the direction estimated as the d axis
for a predetermined time period to be superposed upon a torque voltage,
even when output of a high torque is required. The technique of the
present invention, on the other hand, applies a predetermined detection
voltage in the direction estimated as the q axis under such conditions.
The predetermined detection voltage applied in the direction estimated as
the q-axis direction may be a positive voltage or a negative voltage.
Because of the reasons discussed below, this arrangement enables highly
accurate detection of the electrical angle even when output of a high
torque is required while the synchronous motor is either at a stop or at a
low-speed rotation (hereinafter collectively referred to as under
low-speed operation).
In the specification hereof, the term `superposition` or `to be superposed`
implies that the total of a first voltage and a second voltage is applied.
Namely the term is used in a wider sense than the general meaning of
superposing a signal wave upon a carrier. For example, the expression that
a predetermined negative voltage is superposed and applied in the q-axis
direction is equivalent to that a predetermined voltage is subtracted from
the voltage initially applied in the q-axis direction.
The arrangement of the present invention enables accurate detection of the
electrical angle, because of the following reasons. In order to complete
the present invention, it is naturally required to elucidate the cause
that the conventional method can not successfully detect the electrical
angle under the condition of a high-torque requirement. There have been no
studies on the phenomenon and the cause that the conventional method can
not detect the electrical angle when a high torque is required The
inventors of the present invention have elucidated the cause of
unsuccessful detection of the electrical angle through a variety of
experiments and analyses as discussed below.
As described previously, the electrical angle detection apparatus, which
adopts the conventional technique of electrical angle detection, applies a
detection voltage .DELTA.V.gamma. in the .gamma.-axis direction shown in
FIG. 4. It is here assumed that an error of the electrical angle occurs in
the direction of rotation from the .gamma. axis to the d axis shown in
FIG. 4, that is, in the direction of rotating the rotor, as the positive
direction. Voltages .DELTA.Vd and .DELTA.Vq applied to the d axis and the
q axis according to the detection voltage .DELTA.V.gamma. are respectively
expressed as Equations (1) given below:
.DELTA.Vd=.DELTA.V.gamma..multidot.cos.DELTA..theta.
.DELTA.Vq=-.DELTA.AV.gamma..multidot.sin.DELTA..theta. (1)
Electric currents .DELTA.Id and .DELTA.Iq flowing in the directions of the
d axis and the q axis corresponding to the applied voltages .DELTA.Vd and
.DELTA.Vq are expressed as Equations (2) given below:
.DELTA.Id=.DELTA.V.gamma..multidot.t.multidot.cos.DELTA..theta./Ld
.DELTA.Iq=-.DELTA.V.gamma..multidot.t.multidot.sin.DELTA..theta./Lq(2)
where Ld and Lq respectively denote the inductances in the d-axis direction
and in the q-axis direction, and t denotes the time elapsing after
application of the voltage.
The electric currents .DELTA.Id and .DELTA.Iq are converted into electric
currents .DELTA.I.gamma. and .DELTA.I.delta. flowing in the directions of
the .gamma. axis and the .delta. axis, which are estimated by the
electrical angle detection apparatus, as expressed by Equations (3) and
(4) given below. For the purpose of reference, FIG. 7 shows variations in
electric currents in the .gamma.-axis direction and the .delta.-axis
direction when the voltage .DELTA.V.gamma. is applied in the .gamma.-axis
direction.
##EQU1##
where A=(1/Ld+1/Lq)2 and .DELTA.I=(1/Ld-1/Lq)/2. In the salient pole-type
motor shown in FIGS. 3 and 4, the inductances satisfy the relation of
Ld<Lq, so that .DELTA.I>0.
Equations (3) and (4) show that the electric currents .DELTA.I.gamma. and
.DELTA.I.delta. in the .gamma.-axis direction and the .delta.-axis
direction periodically vary with a variation in angular error
.DELTA..theta. of the electrical angle. FIG. 8 shows the periodical
variations in electric currents. The graph of FIG. 8 shows a value
.DELTA.I.gamma.A, which is obtained by shifting the electric current
.DELTA.I.gamma. according to an equation of
.DELTA.I.gamma.A=.DELTA.I.gamma.-.DELTA.V.gamma..multidot.t.multidot.A. In
a relatively small range of the angular error .DELTA..theta., an
approximate equation of .DELTA..theta.=tan(2.DELTA..theta.)2 is valid. The
angular error .DELTA..theta. is then calculated according to this
approximate equation and Equations (3) and (4) given above. Since it is
required to calculate the angular error .DELTA..theta. in a relatively
small range, the method divides the angular error .DELTA..theta. into
sixteen divisions shown in FIG. 8 and specifies the division where the
angular error .DELTA..theta. exists according to the positive and negative
signs of .DELTA.I.gamma.A+.DELTA.I.delta. and
.DELTA.I.gamma.A-.DELTA.I.delta.. The method carries out the arithmetic
operations after shifting the angular error .DELTA..theta. corresponding
to the specified division. By way of example, when it is determined that
the angular error .DELTA..theta. exists in the division 10 shown in FIG.
8, .DELTA..theta. in Equations (3) and (4) is replaced with
.DELTA..theta.-.pi./4 as shown in Equations (5) and (6) given below:
.DELTA.I.gamma.=.DELTA.V.gamma..multidot.t(A+.DELTA.I.multidot.cos2(.DELTA.
.theta.-.pi./4)) (5)
.DELTA.I.delta.=.DELTA.V.gamma..multidot.t.multidot..DELTA.I.multidot.sin2(
.DELTA..theta.-.pi./4) (6)
In this example, the method calculates .DELTA..theta.-.pi./4 according to
Equations (5) and (6) and determines .DELTA..theta. by adding .pi./4 to
the result of the arithmetic operation. This example regards the case in
which there is a positive angular error .DELTA..theta. (the angular error
in the direction of rotation from the .gamma. axis to the d axis in FIG.
4). The angular error .DELTA..theta. can also be determined in the case
where there is a negative angular error .DELTA..theta. (the angular error
in the reverse direction).
This method is on the assumption that the inductances satisfy the relation
of Ld<Lq and .DELTA.l is greater than zero. When Ld=Lq, .DELTA.I becomes
equal to zero. In this case, .DELTA.I.gamma.A and .DELTA.I.delta. are
constant irrespective of the value of .DELTA..theta. as clearly understood
from Equations (3) and (4), and thereby the angular error .DELTA..theta.
can not be calculated. When Ld>Lq and .DELTA.I<0, the positive and
negative of .DELTA.I.gamma.A and .DELTA.I.delta. are reversed in the graph
of FIG. 8. In this case, the division can not be specified accurately
based on the positive and negative signs of
.DELTA.I.gamma.A+.DELTA.I.delta. and .DELTA.I.gamma.A-.DELTA.I.delta..
Application of the same method as that for the case of .DELTA.I>0 results
in mistakenly specify the division where the angular error .DELTA..theta.
exists, which is deviated by 90 degrees from the true division. This
causes a deviation of the calculated electrical angle by 90 degrees from
the true electrical angle.
When a small torque is required for the motor, the inductances satisfy the
relation of Ld<Lq and no such problems arise. When a large torque is
required for the motor, on the other hand, the inductances may be under
the condition of Ld.gtoreq.Lq. This state is described with the graph of
FIG. 12, which shows a variation in magnetic flux density B plotted
against the strength of an externally generating magnetic field H in the
stator of the motor. The externally generating magnetic field H includes a
magnetic field produced by permanent magnets of the motor and a magnetic
field produced by the electric currents flowing through the windings. The
former magnetic field has a fixed strength as long as the strength is
divided into the d axis and the q axis. It may thus be considered that the
graph of FIG. 12 shows the effect of the electric currents flowing through
the windings on the magnetic flux density. In the graph of FIG. 12, the
slopes of the tangents at the respective points of a curve Cd
corresponding to the d axis and a curve Cq corresponding to the q axis
denote the inductances Ld and Lq.
As shown by the curve Cq in the graph of FIG. 12, the magnetic flux density
keeps linearity in a range A where the externally generating magnetic
field H has a relatively low strength, but causes saturation and becomes
non-linear in a range B where the magnetic field H has the strength of or
above a predetermined level. When a small torque is required for the
motor, the magnetic flux density is in the range A, where the inductances
of the d axis and the q axis are different from each other as shown by
points a1 and a2 in FIG. 12. This enables detection of the electrical
angle. With an increase in torque required for the motor, the electric
currents flowing through the windings of the motor increase to enhance the
strength of the externally generating magnetic field H. The magnetic flux
density accordingly reaches the non-linear range B. The tangent at a point
b is parallel to the curve Cd. At this point, the inductances accordingly
hold the relation of Lq=Ld. With a further increase in required torque,
the magnetic flux density shifts from the point b to a point c and the
relation of the inductances is inverted to Lq<Ld as shown in FIG. 12.
The conventional method of detecting the electrical angle is adopted for
the motors that have sufficiently marginal rating relative to the torque
command value. Namely application of the conventional method is on the
assumption that the magnetic flux density of the motor is within the
linear range A shown in FIG. 12 and that the inductance has a fixed value.
Reduction of the size of the motor results in unsuccessful detection of
the electrical angle under the requirement of a high torque. The inventors
of the present invention have carried out a variety of experiments and
analyses to elucidate the cause of the unsuccessful detection. Lots of
factors may be regarded as the cause that the electrical angle can not be
detected under the requirement of a high torque. The inventors have
elucidated that the fundamental cause of the unsuccessful detection of the
electrical angle is that the magnetic flux saturation under the
high-torque condition inverts the relation of the inductances in the
d-axis direction and the q-axis direction from that under the low-torque
condition.
The inventors of the present invention have studied a variation in q-axis
electric current corresponding to the detection voltage in the state of
magnetic flux saturation, in addition to the elucidation of the cause. It
has then been found that there is an unequivocal relationship between the
q-axis electric current and the angular error of the estimated electrical
angle from the true electrical angle on application of the voltage to the
q axis with respect to a variety of torque command values as shown in the
graph of FIG. 18. FIG. 18 shows the angular error of the electrical angle
as abscissa and the q-axis electric current as ordinate with respect to a
variety of torque command values. Parameters i1, i2, . . . represent the
electric currents flowing through the q axis corresponding to the torque
command values, and the torque command value increases in this sequence.
The present invention is based on the cause and the unequivocal
relationship discussed above. In the present invention, the voltage
applied to the q axis may be positive or negative. The following describes
the reason why the electrical angle can be detected with a high accuracy
in the respective cases. The first description regards the case in which a
negative voltage is applied to the q axis.
Application of a negative voltage aims to cancel the effect of the magnetic
saturation on detection of the electrical angle. When a voltage is applied
in the negative direction, the strength of the externally generating
magnetic field decreases in the q-axis direction. Such a decrease enables
detection of the electric current in the linear range A shown in FIG. 12
and causes the inductances to satisfy the relation of Ld<Lq. This enables
the electrical angle to be detected even under the requirement of a high
torque. The magnitude of the negative voltage to be superposed may be
determined experimentally or arithmetically, in order to attain sufficient
relieve of the magnetic flux saturation, based on the characteristics of
magnetic flux saturation of the stator.
The following briefly describes calculation of the angular error
.DELTA..theta. of the electrical angle on application of a voltage to the
q axis, although the details of the calculation will be discussed later.
When a predetermined negative voltage is applied to the q axis, Equations
(7) and (8) given below are valid as corresponding to Equations (3) and
(4) discussed above in the case where a voltage is applied to the d axis:
.DELTA.I.gamma.=.DELTA.V.delta..multidot.t.multidot..DELTA.I.multidot.sin2.
DELTA..theta. (7)
.DELTA.I.delta.=.DELTA.V.delta..multidot.t.multidot..DELTA.I.multidot.(A.mu
ltidot.cos2.DELTA..theta.) (8)
where A=(1/d+1/Lq)/2 and .DELTA.I=(1/Ld-1/Lq)/2, and .DELTA.V.delta.
denotes the absolute value of the predetermined negative voltage. The
angular error .DELTA..theta. of the electrical angle can thus be
calculated from the observed electric currents .DELTA.I.delta. and
.DELTA.I.delta..
The electrical angle computation unit in the electrical angle detection
apparatus of the present invention may apply any one of the available
techniques that determine a deviation of the estimated electrical angle
from the true electrical angle based on variations in d-axis electric
current and q-axis electric current and thereby calculate the electrical
angle of the motor. The above calculation is one example of such available
techniques.
It is desirable that a negative detection voltage is applied only when the
torque command value is not less than a predetermined level.
The structure of the present invention applies a negative voltage to the q
axis, which is a main dominant factor of the motor torque. This may cause
some decrease in torque in the process of detecting the electrical angle.
Application of the negative voltage in the q-axis direction only when the
torque command value of the motor is not less than a predetermined level
effectively minimizes the torque variation in the course of detection of
the electrical angle. The predetermined level of the torque may be
specified as the upper limit of the torque command value that allows
detection of the electrical angle by another process, for example, by
application of a voltage to the d axis. When the torque command value is
less than the predetermined level, detection of the electrical angle may
follow the conventional method or the method proposed by the applicant of
the present invention as disclosed in JAPANESE PATENT LAID-OPEN GAZETTE
No. 7-177788.
It is also desirable that at least one of the absolute value of the
detection voltage and the time period of voltage application monotonously
decreases with a decrease in torque command value.
The inductance Lq in the q-axis direction should be in the linear range A
shown in FIG. 12, in order to enable detection of the electrical angle
under the high-torque condition. As clearly understood from the graph of
FIG. 12, the absolute value of the voltage to be superposed to make the
inductance Lq in the q-axis direction in the linear range A varies with a
variation in torque required for the motor. By way of example, the voltage
to be superposed should have a large absolute value under the torque
requirement corresponding to the point c and have a small absolute value
under the torque requirement corresponding to the point b. The time period
of voltage application has a similar relationship. A decrease in at least
one of the absolute value of the detection voltage and the time period of
voltage application with a decrease in torque command value required for
the motor effectively minimizes the torque variation due to application of
the detection voltage to the q axis. The monotonous decrease here includes
a linear decrease, a curvilinear decrease, and a stepwise decrease in
absolute value of the applied voltage with a decrease in torque command
value. Either one of the absolute value of the applied voltage and the
time period of voltage application may decrease with a decrease in torque
command value, or alternatively the both may decrease.
In accordance with one preferable application of the present invention, the
method first applies a predetermined negative voltage in the q-axis
direction for a predetermined first time period to be superposed upon the
torque voltage and subsequently applies a predetermined positive voltage
in the q-axis direction for a predetermined second time period.
This structure enables the q-axis electric current that has decreased in
response to application of the negative detection voltage to be recovered
quickly to a predetermined level corresponding to the required torque.
This effectively suppresses the influence of the torque variation in the
course of detection of the electrical angle. The absolute value of the
positive detection voltage and the second time period of voltage
application should be determined by taking into account this effect. It is
not required to make the absolute value of the positive detection voltage
and the second time period of voltage application coincident with the
absolute value of the negative detection voltage and the first time period
of voltage application.
The following describes the case in which a positive voltage is applied to
the q axis. In this case, the method detects the electrical angle by
taking advantage of the unequivocal relationship between the variation in
q-axis electric current and the angular error of the electrical angle
illustrated in the graph of FIG. 18. A concrete procedure provides a
memory that stores the relationship between the angular error obtained as
the deviation of the estimated electrical angle from the true electrical
angle and the variation in q-axis electric current corresponding to the
detection voltage. The method refers to the stored relationship and reads
the angular error corresponding to the observed variation in electric
current due to application of the detection voltage in the q-axis
direction. The electrical angle is calculated from the angular error thus
obtained.
As described previously, the unequivocal relationship is valid under the
condition of magnetic saturation. The relationship is stored in advance
into the memory, for example, in the form shown in the graph of FIG. 18.
The method reads the angular error from the relationship stored in the
memory and thereby determines the electrical angle. The relationship shown
in FIG. 18 may be stored in the form of a table or in the form of an
approximate function.
The reason why there is an unequivocal relationship between the q-axis
electric current and the angular error of the electrical angle under the
condition of the magnetic flux saturation has not completely been
elucidated, but the following is presumed to be the reason. FIG. 19 shows
the state of a magnetic filed in the course of detection of the electrical
angle. The composite magnetic field occurs in the motor, which is the
combination of the magnetic field produced by the permanent magnets on the
rotor with the magnetic field produced by the electric currents flowing
through the windings. When the estimated electrical angle has no angular
error, application of a voltage to the q axis causes a magnetic field
expressed by a vector q1 in the q-axis direction as shown in FIG. 19. The
combination of the magnetic field of the vector q1 with a magnetic field
of the permanent magnets expressed by a vector d1 gives a composite
magnetic field expressed by a vector .phi.1. The strength of the magnetic
field .phi.1 is expressed by Equation (9) given below:
.phi.1=.sqroot.(d1.sup.2 +q1.sup.2) (9)
When the estimated electrical angle has an angular error, on the other
hand, the applied voltage causes a magnetic field expressed by a vector
.delta.1 in the .delta.-axis direction. The combination of the magnetic
field of the vector .delta.1 with the magnetic field of the permanent
magnets expressed by the vector d1 gives a composite magnetic field
expressed by a vector .phi.2. The supplied electric current in this case
is identical with that in the case where the estimated electrical angle
has no angular error. The magnitude of the vector q1 is accordingly equal
to the magnitude of the vector .delta.1. When the magnitudes of these
vectors are shown as q1, the strength of the magnetic field .phi.2 is
expressed by Equation (10) given below:
.phi.2=.sqroot.(d1.sup.2 +q1.sup.2
+2d1.multidot.q1.multidot.sin.DELTA..theta.) (10)
Comparison between Equations (9) and (10) shows that the magnitude of the
vector .phi.2 is greater than the magnitude of the vector .phi.1 when the
angular error .DELTA..theta. is a positive value. This means that the
magnetic flux density further increases according to the angular error in
the state that the magnetic field causes magnetic saturation (that is, in
the range B of FIG. 12). The increase in magnetic flux density in the
range B of FIG. 12 decreases the inductance and enhances the flow of
electric current. This mechanism may be the reason why there is an
equivocal relationship between the q-axis electric current and the angular
error as shown in the graph of FIG. 18.
When the method takes advantage of this unequivocal relationship, it is
desirable that the detection voltage is positive. A negative detection
voltage may, however, be applicable in the range that causes magnetic
saturation. Application of a positive voltage causes the q-axis electric
current to keep the required level corresponding to the torque command
value and thereby prevents the torque deficiency in the course of
detection of the electrical angle. One possible modification applies the
detection voltage to the q axis only under the high-torque condition that
causes magnetic saturation. The conventional method is applied to detect
the electrical angle in the other state.
Regulation of the electric currents flowing through the windings based on
the electrical angle controls operation of the synchronous motor. The
technique regarding the detection of the electrical angle is accordingly
applicable to control of the synchronous motor. This technique enables
appropriate control of the synchronous motor even when a high torque is
required in the state of low-speed operation.
The principle of the present invention is applicable to not only the inner
rotor-type synchronous motor, which has a rotor on the center and a stator
on the circumference thereof, but also the outer rotor-type synchronous
motor. The outer rotor-type synchronous motor has a stator on the center
and a ring-shaped outer rotor surrounding the stator. In the outer
rotor-type synchronous motor, control electric currents are flown through
three-phase coils to form a revolving magnetic field and thereby rotate
the ring-shaped outer rotor.
These and other objects, features, aspects, and advantages of the present
invention will become more apparent from the following detailed
description of the preferred embodiments with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram schematically illustrating the structure of a
motor control apparatus 10 as a first embodiment according to the present
invention;
FIG. 2 schematically illustrates the structure of a three-phase synchronous
motor 40;
FIG. 3 is an end view showing the positional relationship between a stator
30 and a rotor 50 in the three-phase synchronous motor 40;
FIG. 4 is an equivalent circuit diagram of the three-phase synchronous
motor 40;
FIG. 5 is a flowchart showing a motor control routine under low-speed
operation;
FIG. 6 is a flowchart showing the details of an electrical angle detection
process under a low-torque condition executed at step S300 in the
flowchart of FIG. 5;
FIG. 7 shows the applied voltage and the observed electric currents in the
electrical angle detection process under the low-torque condition;
FIG. 8 is a graph showing the observed electric currents plotted against
the angular error in the electrical angle detection process under the
low-torque condition;
FIG. 9 is a flowchart showing the details of an electrical angle detection
process under a high-torque condition executed at step S400 in the
flowchart of FIG. 5;
FIG. 10 shows the applied voltage and the observed electric currents in the
electrical angle detection process under the high-torque condition;
FIG. 11 is a graph showing the observed electric currents plotted against
the angular error in the electrical angle detection process under the
high-torque condition;
FIG. 12 is a graph showing the magnetic saturation characteristics of the
three-phase synchronous motor 40;
FIG. 13 shows the timing of the motor current control process;
FIG. 14 is a graph showing a first relationship between the torque command
value and the applied voltage .DELTA..delta.;
FIG. 15 is a graph showing a second relationship between the torque command
value and the applied voltage .DELTA..delta.;
FIG. 16 is a graph showing a third relationship between the torque command
value and the applied voltage to .DELTA..delta.;
FIG. 17 is a flowchart showing the details of another electrical angle
detection process under a high-torque condition executed at step S400 in
the flowchart of FIG. 5 as a second embodiment according to the present
invention;
FIG. 18 is a graph showing the variation in electric current plotted
against the angular error; and
FIG. 19 shows the relationship between the angular error and the magnetic
field under the high-torque condition.
DESCRIPTION OF THE PREFERRED EMBODIMENT
1. Structure of Embodiment
The general structure of a three-phase synchronous motor 40 is described
with the drawing of FIG. 2. The three-phase synchronous motor 40 includes
a stator 30, a rotor 50, and a casing 60 for accommodating the stator 30
and the rotor 50 therein. The rotor 50 has permanent magnets 51 through 54
attached to the outer circumference thereof and is provided with a
rotating shaft 55. The rotating shaft 55 passes through the anal center of
the rotor 50 and is rotatably supported by bearings 61 and 62 disposed in
the casing 60.
The rotor 50 is prepared by laying a plurality of plate-like rotor elements
57, which are punched out of a non-directional electromagnetic steel
plate, one upon another. Each rotor element 57 has four salient poles 71
through 74 arranged in a cross configuration as shown in FIG. 3. The
rotating shaft 55 is pressed into the laminate of the rotor elements 57,
so as to temporarily fix the laminate of the rotor elements 57. Each rotor
element 57 composed of the electromagnetic steel plate has an insulating
layer and an adhesive layer formed on the surface thereof. The laminate of
the rotor elements 57 is heated to a predetermined temperature, which
fuses the adhesive layers and thereby fixes the laminate of the rotor
elements 57.
After the assembly of the rotor 50, the permanent magnets 51 through 54 are
attached to the outer circumferential surface of the rotor 50 along the
axis of the rotor 50 at the positions between the salient poles 71 through
74. The permanent magnets 51 through 54 are magnetized in the radial
direction of the rotor 50 in such a manner that the adjoining magnets form
magnetic poles of different polarities. For example, the outer
circumferential face of the permanent magnet 51 forms an N pole, whereas
the outer circumferential face of the adjoining permanent magnet 51 forms
an S pole. In the state that the rotor 50 is combined with the stator 30,
the pair of the permanent magnets 51 and 52 form a magnetic path Md that
passes through the rotor elements 57 and stator elements 20 (described
below) as shown by the one-dot chain line in FIG. 3.
The stator 30 is prepared by laying a plurality of plate-like stator
elements 20, which are punched out of a non-directional electromagnetic
steel plate like the rotor elements 57, one upon another. Each stator
element 20 has twelve teeth 22 as shown in FIG. 3. Coils 32 for causing
the stator 30 to generate a revolving magnetic field are wound on slots 24
formed between the teeth 22. Bolt holes, each of which receives a fixation
bolt 34, are formed in the outer circumference of the stator element 20,
although being omitted from the illustration of FIG. 3.
The stator 30 is temporarily fixed by heating the laminate of the stator
elements 20 under pressure and fusing the adhesive layers thereof. In this
state, the coils 32 are wound on the teeth 22 to complete the stator 30.
The stator 30 is then placed in the casing 60 and fixed to the casing 60
by fitting the fixation bolts 34 in the bolt holes. The rotor 50 is then
rotatably attached to the casing 60 by means of the bearings 61 and 62.
This completes the assembly of the three-phase synchronous motor 40.
When an excitation current is flown to generate a revolving magnetic field
on the stator coils 32 of the stator 30, a magnetic path Mq is formed to
pass through the adjoining salient poles as well as the rotor elements 57
and the stator elements 20 as shown by the two-dot chain line in FIG. 3.
The axis `d` represents the axis through which the magnetic flux formed by
the permanent magnet 52 passes in the radial direction of the rotor 50,
whereas the axis `q` represents the axis through which the magnetic flux
formed by the stator coils 32 of the stator 30 passes in the radial
direction of the rotor 50. The d axis and the q axis are axes of rotation
with rotation of the rotor 50. In this embodiment, the outer
circumferential faces of the permanent magnets 51 and 53 attached to the
rotor 50 form N poles, whereas the outer circumferential faces of the
permanent magnets 52 and 54 form S poles. The geometrical angle of the d
axis and the q axis is accordingly 45 degrees as shown in FIG. 3. FIG. 4
shows an equivalent circuit of the three-phase synchronous motor 40 of
this embodiment. The three-phase synchronous motor 40 is expressed by an
equivalent circuit including three-phase coils of U, V, and W phases and a
permanent magnet rotating about an axis of rotation. In the equivalent
circuit, the d axis is defined as the axis that passes through the N pole
of the permanent magnet as the positive direction, whereas the q axis is
defined as the axis that is not only electrically but geometrically
perpendicular to the d axis. The electrical angle is given as a rotational
angle .theta. of the axis that passes through the U-phase coil and the d
axis.
FIG. 1 shows the structure of a motor control apparatus 10. The motor
control apparatus 10 includes a control ECU 100 that regulates the motor
currents supplied to the three phases, U, V, and W phases of the
three-phase synchronous motor 40 in response to an external torque
instruction, electric current sensors 102, 103, and 104 that respectively
measure a U-phase current Au, a V-phase current Av, and a W-phase current
Aw of the three-phase synchronous motor 40, filters 106, 107, and 108 that
eliminate high-frequency noises from the observed electric currents, and
three analog-digital converters (ADC) 112, 113, and 114 that convert the
observed electric currents to digital data.
The control ECU 100 includes a microprocessor (CPU) 120 that carries out
arithmetic and logic operations, a ROM 122 in which the processing of the
CPU 120 and required data are stored in advance, a RAM 124, which data
required for the processing are temporarily written in and read from, and
a clock 126 that counts the time. These elements are mutually connected
via a bus. An input port 116 and an output port 118 are also connected to
the bus. The CPU 120 reads the observed electric currents Au, Av, and Aw
flowing through the respective phases, U, V, and W phases, of the
three-phase synchronous motor 40 via these ports 116 and 118.
The control ECU 100 has a voltage application unit 130 arranged on its
output side. The voltage application unit 130 applies voltages between the
respective coils of the three-phase synchronous motor 40, so as to obtain
the phase currents Au, Av, and Aw of the three-phase synchronous motor 40
determined corresponding to an independently input torque command value.
The CPU 120 gives control outputs Vu, Vv, Vw, and SD to the voltage
application unit 130, in order to externally regulate the voltages applied
to the respective coils of the three-phase synchronous motor 40.
Among the various elements of the motor control apparatus 10 described
above, the electric current sensors 102 through 104, the filters 106
through 108, the ADCs 112 through 114, the voltage application unit 130,
and the control ECU 100 constitute the electrical angle detection
apparatus of the present invention.
2. Motor Currents Control Process
The motor control apparatus 10 of the embodiment controls the electric
currents as described below with the drawing of FIG. 4. The flow of the
electric current Au through the U phase causes a magnetic field, which
passes through the U phase and has the strength that varies with the
magnitude of the electric current Au. The U-phase current Au is
accordingly expressed as a vector having the direction of the magnetic
field and the magnitude Au. In a similar manner, the V-phase current Av
and the W-phase current Aw flowing through the V phase and the W phase are
expressed as vectors. An arbitrary electric current vector in the plane is
given as the sum of electric current vectors in representative two
directions. The representative two directions are, for example, a
direction .alpha. and a direction .beta. shown in FIG. 4. The electric
current vector corresponding to a magnetic field occurring in an arbitrary
direction in the plane of rotation of the motor is expressed by electric
currents A.alpha. and A.beta. flowing through the two-phase coils. In
accordance with a concrete procedure, the electric currents A.alpha. and
A.beta. that are equivalent to certain electric currents Au, Av, and Aw
are expressed by Equations (11) given below:
A.alpha.=Au-Av/2-Aw/2
A.beta.=(.sqroot.3).multidot.(Aw-Av)/2 (11)
In the case where A.alpha. and A.beta. are known, on the contrary, the
respective phase currents Au, Av, and Aw are determined by Equations (12)
given below, based on the condition that the total of the electric
currents of the U, V, and W phases is equal to zero (Au+Av+Aw=0).
Au=2(.sqroot.3-3).multidot.A.alpha./
Av=(3-.sqroot.3).multidot.(A.alpha.-A.beta.)/3
Aw=(3-.sqroot.3).multidot.(A.alpha.+A.beta.)/3 (12)
This is the generally known three phase-to-two phase conversion. The
following describes the procedure of controlling the electric currents in
the three-phase synchronous motor 40 with the electric currents A.alpha.
and A.beta. after the three phase-to-two phase conversion.
The electric current vectors may be defined with respect to the magnetic
fields occurring in the d-axis direction and the q-axis direction of FIG.
4. Magnitudes Ad and Aq of the electric current vectors in the d-axis
direction and the q-axis direction are expressed with the electric
currents A.alpha. and A.beta. in the direction .alpha. and the direction
.beta. as Equations (13) given below:
Ad=A.alpha..multidot.cos.theta.+A.beta..multidot.sin.theta.
Aq=-A.alpha..multidot.sin.theta.+A.beta..multidot.cos.theta.(13)
In the case where Ad and Aq are known, in the contrary, A.alpha. and
A.beta. are determined by Equations (14) given below:
A.alpha.=Ad.multidot.cos.theta.-Aq.multidot.sin.theta.
A.beta.=Ad.multidot.sin.theta.+Aq.multidot.cos.theta. (14)
Specification of the electric currents flowing in the d-axis direction and
the q-axis direction in the three-phase synchronous motor 40 determines
the two-phase electric currents A.alpha. and A.beta. according to
Equations (14) and the electric currents to be actually flown through the
U, V, and W phases according to Equations (12). This also determines the
voltages to be applied to the U, V, and W phases. The control of the
electric currents in the three-phase synchronous motor 40 is based on this
idea. Another possible arrangement directly specifies the relationship
between the electric currents in the d-axis direction and the q-axis
direction and the U, V, and W phase currents, without using the electric
current vectors in the directions .alpha. and .beta.. In the following
description, for example, the `d-axis electric current and the q-axis
electric current` imply the magnitude of the electric current vectors
based on the idea discussed above. When the electric current flowing
through the synchronous motor is divided into the d-axis direction and the
q-axis direction, the q-axis electric current is a main dominant factor of
the torque of the synchronous motor 40 as is generally known.
3. Motor Control Routine under Low-Speed Operation in First Embodiment
FIG. 5 is a flowchart showing a motor control routine under low-speed
operation, which is executed in the first embodiment to control the
three-phase synchronous motor 40 that is in the state of low-speed
operation. The CPU 120 of the control ECU 100 shown in FIG. 1 periodically
executes this motor control routine under low-speed operation together
with other control routines (not shown).
When the program enters the motor control routine under low-speed operation
shown in the flowchart of FIG. 5, the CPU 120 first reads the torque
command value at step S100 and compares the input torque command value
with a predetermined torque T1 at step S200. An appropriate process is
applied to detect the electrical angle according to the magnitude of the
torque command value as discussed later. The torque command value may be
input externally via the input port 116 or may be computed by the CPU 120
based on a variety of externally input data. It is desirable to set a
hysteresis for the comparison at step S200, in order to prevent chattering
in the case where the torque command value is dose to the predetermined
torque T1.
The predetermined torque T1 may be determined experimentally as a specific
torque, to which an electrical angle detection process under a low-torque
condition discussed below is not applicable. In this embodiment, the
predetermined torque T1 is set to be a little smaller than the specific
torque, in order to assure the detection of the electrical angle.
When the input torque command value is not greater than the predetermined
torque T1 at step S200, the CPU 120 executes an electrical angle detection
process under a low-torque condition at step S300. The following describes
the details of the electrical angle detection process under the low-torque
condition with the flowchart of FIG. 6 and the graph of FIG. 7. The
flowchart of FIG. 6 shows a routine of the electrical angle detection
process under the low-torque condition. The graph of FIG. 7 shows the
voltage pulses applied in the direction of a .gamma. axis and the electric
currents flowing through the d axis and the q axis in the electrical angle
detection process under the low-torque condition.
When the program enters the electrical angle detection routine under the
low-torque condition, the CPU 120 first detects initial values I.gamma.0
and I.delta.0 of the electric currents flowing in the directions of a
.gamma. axis and a .delta. axis at step S305. The CPU 120 receives signals
output from the electric current sensors 102, 103, and 104, which measure
the electric currents of the U, V, and W phases, via the filters 106, 107,
and 108, the ADCs 112, 113, and 114, and the input port 116, and converts
the input electric currents of the U, V, and W phases into the electric
currents in the .gamma.-axis direction and the .delta.-axis direction
based on the arithmetic operations discussed in the section "2. Motor
Currents Control Process". Since the d axis and the q axis can be defined
only after the determination of the electrical angle of the synchronous
motor 40 as shown in FIG. 4, the CPU 120 estimates the .gamma. axis and
the .delta. axis based on an estimated electrical angle .theta.c and
determine the electric currents in the .gamma.-axis direction and the
.delta.-axis direction. There is accordingly an angular error
.DELTA..theta. between the estimated electrical angle .theta.c and an
actual electrical angle .theta. as shown in FIG. 4. In the initial state,
a positive electric current flows through the .delta. axis corresponding
to the torque command value, whereas a negative electric current flows
through the .gamma. axis as shown in the graph of FIG. 7. The flow of the
negative electric current through the .gamma. axis, that is, the flow of
the electric current in the negative direction of the d axis, causes a
positive reluctance torque to occur in the motor that has an inductance Ld
in the d-axis direction smaller than an inductance Lq in the q-axis
direction, for example, in the synchronous motor 40 of the embodiment.
The CPU 120 then outputs a voltage .DELTA.V.gamma. in the .gamma.-axis
direction at step S310, waits for elapse of a sampling time ts at step
S315, and detects electric currents I.gamma.1 and I.delta.1 at step S320.
The sampling time ts for measuring the electric current is set
experimentally as the value that enables a variation in electric current
flowing through the coil windings to be detected sufficiently. The
conditions to be considered for setting the sampling time will be
discussed later. The wait for elapse of the sampling time ts (step S315)
is realized by interrupting another routine, which is executed by the CPU
120 for controlling operation of the synchronous motor 40, at every
sampling time ts and executing this routine. The voltage .DELTA.V.gamma.
applied in the .gamma.-axis direction is superposed upon the voltage
applied in the .gamma.-axis direction in the initial state as shown in
FIG. 7. This is equivalent to an increase in voltage applied in the
.gamma.-axis direction by .DELTA..gamma..
A voltage is applied in the .gamma.-axis direction since the electric
current in the q-axis direction is a main dominant factor of the torque
and the electric current in the d-axis direction has a relatively small
effect on the torque in the synchronous motor 40 of the embodiment. The
flow of the electric current in the .gamma.-axis direction, which is
estimated as the d-axis by the control ECU 100, reduces the effect on the
torque to a relatively small level in the process of detection of the
electrical angle. Although a significant variation in electric current in
the .delta.-axis direction is shown in the graph of FIG. 7 for convenience
of explanation, the variation is very small in the actual state.
The CPU 120 subsequently outputs a voltage -.DELTA.V.gamma. in the
.gamma.-axis direction at step S325, waits for elapse of the sampling time
ts at step S330, and detects electric currents I.gamma.2 and I.delta.2 at
step S335. The voltage -.DELTA.V.gamma. applied in the .gamma.-axis
direction is superposed upon the voltage in the initial state. As clearly
shown in FIG. 7, this is equivalent to subtraction of 2..DELTA.V.gamma.
from the voltage applied in the .gamma.-axis direction at the time point
when the electric currents I.gamma.1 and I.delta.1 are detected or to
subtraction of .DELTA.V.gamma. from the voltage applied in the initial
state.
In this embodiment, the sampling time ts at step S330 is set equal to the
sampling time ts at step S315 for the interrupt of another routine
executed by the CPU 120. These sampling times may, however, be different
from each other. The sampling time may not be a fixed time period but may
be a fixed cycle; for example, the electric currents may be detected at
the time point when the CPU 120 completes another routine.
The CPU 120 calculates variations in electric currents from the observed
electric currents at step S340. A concrete procedure determines variations
in electric currents .DELTA.I.gamma. and .DELTA.I.delta. by respectively
averaging variations .DELTA.I.gamma.1 (=I.gamma.1-I.gamma.0 ) and
.DELTA.I.delta. (=I.delta.1-I.delta.0) between the initial electric
currents and the observed electric currents at step S320 and variations
.DELTA.I.gamma.2 (=I.gamma.2-I.gamma.1) and .DELTA.I.delta.2
(=I.delta.2-I.delta.1) between the observed electric currents at step S320
and the observed electric currents at step S335. Averaging the variations
in electric currents improves the accuracy of detection of the variations
in electric currents. Equations (15) given below are used to calculate the
mean variations in electric currents by considering the signs of
.DELTA.I.gamma.1, .DELTA.I.delta.1, .DELTA.I.gamma.2, and
.DELTA.I.delta.2:
.DELTA.I.gamma.=(.DELTA.I.gamma.1-.DELTA.I.gamma.2)/2
.DELTA.I.delta.=(.DELTA.I.delta.1-.DELTA.I.delta.2)/2 (15)
In this embodiment, the sampling times at step S315 and at step 330 are set
to the identical fixed value ts, the variations in electric currents
.DELTA.I.gamma. and .DELTA.I.delta. are determined respectively as the
means of .DELTA.I.gamma.1 and .DELTA.I.gamma.2 and .DELTA.I.delta.1 and
.DELTA.I.delta.2. When the sampling times are different from each other,
on the other hand, .DELTA.I.gamma.1, .DELTA.I.delta.1, .DELTA.I.gamma.2,
and .DELTA.I.delta.2 are respectively divided by the sampling times and
converted to the rates of change in electric currents, prior to the
calculation of the means. In the case where a transistor inverter is
applied for the voltage application unit 130 shown in FIG. 1, the dead
time loss may cause the time for which the voltage is actually applied to
the coil windings to be made longer or shorter than the expected time. In
this case, correction equations may be used to determine the accurate
variations in electric currents.
As discussed later, the ratio of the variations in electric currents
.DELTA.I.gamma. and .DELTA.I.delta. is required for determination of the
electrical angle. One possible modification accordingly omits the
processing of steps S325 through S335 from the routine of FIG. 6 and
calculates the ratio of the variations in electric currents
.DELTA.I.gamma. and .DELTA.I.delta. only from the observed variations
.DELTA.I.gamma.1 and .DELTA.I.delta.1. This procedure desirably shortens
the time required for detection of the electrical angle. This procedure is
especially preferable when the errors included in the observed variations
.DELTA.I.gamma.1 and .DELTA.I.delta.1 coincide with each other and can be
compensated by calculating the ratio of the variations .DELTA.I.gamma.1
and .DELTA.I.delta.1.
The CPU 120 specifies a division where the angular error .DELTA..theta.
between the estimated electrical angle .theta.c and the actual electrical
angle .theta. exists, based on the calculated variations in electric
currents .DELTA.I.gamma. and .DELTA.I.delta. at step S345. The concrete
procedure of specifying the division is described with the graph of FIG.
8. FIG. 8 shows the variations in electric currents plotted against the
angular error .DELTA..theta. (=.theta.-.theta.c) between the electrical
angle .theta.c estimated by the CPU 120 and the true electrical angle
.theta.. The variations in electric currents .DELTA.I.gamma. and
.DELTA.I.delta. are expressed respectively by Equation (3)
.DELTA.I.gamma.=.DELTA.V.gamma..multidot.t(A+.DELTA.I.multidot.cos2.DELTA.
.theta.) and Equation (4)
.DELTA.I.delta.=.DELTA.V.gamma..multidot.t.multidot..DELTA.I.multidot.sin2
.DELTA..theta. given above, where A=(1/Ld+1/Lq)/2 and
.DELTA.I=(1/Ld-1/Lq)/2. When
.DELTA.I.gamma.A=.DELTA.I.gamma.-.DELTA.V.gamma..multidot.t.multidot.A,
.DELTA.I.gamma.A is expressed as Equation (16) given below:
##EQU2##
The plots of FIG. 8 show the variations in electric currents
.DELTA.I.gamma.A and .DELTA.I.delta..
The CPU 120 applies the voltage in the .gamma.-axis direction, so that
.DELTA.I.delta.=0 when the angular error .DELTA..theta.=0. As explained
with Equations (4) and (16), .DELTA.I.gamma.A and .DELTA.I.delta.
theoretically vary with variations in the cosine function and the sine
function according to the angular error .DELTA..theta..
The range of -180 degrees to 180 degrees where the angular error
.DELTA..theta. may exist is divided into sixteen as divisions 1 through 16
shown in FIG. 8. The division where the angular error .DELTA..theta.
exists is specified according to the positive and negative signs of
.DELTA.I.gamma.A+.DELTA.I.delta. and .DELTA.I.gamma.A-.DELTA.I.delta. as
follows:
Case 1: when .DELTA.I.gamma.A+.DELTA.I.delta.>0 and
.DELTA.I.gamma.A-.DELTA.I.delta.>0, possible divisions where the angular
error exists are divisions 1, 8, 9, and 16;
Case 2: when .DELTA.I.gamma.A+.DELTA.I.delta.>0 and
.DELTA.I.gamma.A-.DELTA.I.delta.<0, possible divisions where the angular
error exists are divisions 2, 3, 10, and 11;
Case 3: when .DELTA.I.gamma.A+.DELTA.I.delta.<0 and
.DELTA.I.gamma.A-.DELTA.I.delta.<0, possible divisions where the angular
error exists are divisions 4, 5, 12, and 13; and
Case 4: when .DELTA.I.gamma.A+.DELTA.I.delta.<0 and
.DELTA.I.gamma.A-.DELTA.I.delta.>0, possible divisions where the angular
error exists are divisions 6, 7, 14, and 15.
The CPU 120 subsequently calculates the angular error .DELTA..theta.
corresponding to the specified division at step S350. The angular error
.DELTA..theta. is calculated by approximate equations, which are valid in
the range of relatively small .DELTA..theta. and expressed as Equations
(17) through (24) given below corresponding to the respective cases 1
through 4:
Case 1:
.DELTA..theta.=.DELTA.I.delta./(2.multidot..DELTA.I.gamma.A)(17)
.DELTA..theta.=.DELTA.I.delta./(2.multidot..DELTA.I.gamma.A)+.pi.(18)
Case 2:
.DELTA..theta.=-.DELTA.I.gamma.A/(2.multidot..DELTA.I.delta.)+.pi./4(19)
.DELTA..theta.=-.DELTA.I.gamma.A/(2.multidot..DELTA.I.delta.)+5.pi./4(20)
Case 3:
.DELTA..theta.=.DELTA.I.delta./(2.multidot..DELTA.I.gamma.A)+.pi./2(21)
.DELTA..theta.=.DELTA.I.delta./(2.multidot..DELTA.I.gamma.A)+3.pi./2(22)
Case 4:
.DELTA..theta.=-.DELTA.I.gamma.A/(2.multidot..DELTA.I.delta.)+3.pi./4(23)
.DELTA..theta.=-.DELTA.I.gamma.A/(2.multidot..DELTA.I.delta.)+7.pi./4(24)
There are two equations for calculating the angular error .DELTA..theta.
with respect to each of the cases 1 through 4 (for example, Equations (17)
and (18) in the case 1) because of the following reason. In the case 1,
the ratio of the variations in electric currents .DELTA.I.gamma.A and
.DELTA.I.delta. in the division 1 is identical with that in the division 9
as clearly understood from the graph of FIG. 8. Similarly the ratio in the
division 8 is identical with the ratio in the division 16. This means that
the calculation only from .DELTA.I.gamma.A and .DELTA.I.delta. gives two
solutions that are differentiated from each other by .pi..
The technique of the embodiment executes the electrical angle detection
process at the cycle that keeps the angular error in the range of -90
degrees to 90 degrees. The cycle of executing the electrical angle
detection process is accordingly shorter than the time period required for
rotating the synchronous motor 40 by 90 degrees. The sampling times ts at
steps S315 and S330 in the flowchart of FIG. 6 are set equal to several
milliseconds by taking into account this restriction. Because of this
prerequisite, the embodiment calculates the electrical angle only with
Equations (17), (19), (21), and (23).
One possible application carries out determination of the polarity, that
is, determines whether the angular error exists in the range of -90
degrees to 90 degrees or in another range, in addition to the electrical
angle detection process of the embodiment. A variety of techniques may be
adopted for determination of the polarity. Available examples include the
techniques disclosed in JAPANESE PATENT LAID-OPEN GAZETTE No. 7-177788 by
the applicant of the present invention. Determination of the polarity
enables the angular error to be unequivocally determined in the range of
-180 degrees to 180 degrees.
The CPU 120 subsequently corrects the estimated electrical angle .theta.c
with the calculated angular error .DELTA..theta. at step S355. A concrete
procedure sets the sum of .theta.c and .DELTA..theta. to the corrected
electrical angle .theta.c. The program completes the electrical angle
detection process under the low-torque condition at step S300 and returns
to the motor control routine under low-speed operation shown in the
flowchart of FIG. 5. The CPU 120 carries out the motor currents control
process based on the detected electrical angle at step S500. As described
in (2) Motor Currents Control Process, the CPU 120 determines the d-axis
electric current and the q-axis electric current to be flown through the
synchronous motor 40 corresponding to the torque command value and carries
out the two phase-to-three phase conversion, that is, converts the d-axis
electric current and the q-axis electric current into the electric
currents to be flown through the U, V, and W phases.
When the input torque command value is greater than the predetermined
torque T1 at step S200, the CPU 120 executes an electrical angle detection
process under a high-torque condition at step S400. The electrical angle
detection process under the low-torque condition discussed above can not
detect the electrical angle with a high accuracy under the high-torque
condition. The following describes the details of the electrical angle
detection process under the high-torque condition with the flowchart of
FIG. 9 and the graph of FIG. 10. The flowchart of FIG. 9 shows a routine
of the electrical angle detection process under the high-torque condition.
The graph of FIG. 10 shows the voltage pulses applied in the direction of
the .delta. axis and the electric currents flowing through the d axis and
the q axis in the electrical angle detection process under the high-torque
condition.
When the program enters the electrical angle detection routine under the
high-torque condition, the CPU 120 first detects initial values I.gamma.0
and I.delta.0 of the electric currents flowing in the directions of the
.gamma. axis and the .delta. axis at step S405, and applies a voltage
-.DELTA.V.delta. to the .delta. axis at step S410. This is equivalent to
superposition of a negative voltage -.DELTA.N.delta. upon the initial
voltage or subtraction of .DELTA.V.delta. from the initial voltage.
Whereas a positive voltage is superposed and applied to the .gamma. axis
in the electrical angle detection routine under the low-torque condition,
a negative voltage is superposed and applied to the .delta. axis in the
electrical angle detection routine under the high-torque condition.
When a high torque is required, a large electric current flows in the
direction of the .delta. axis in the initial state. This causes magnetic
saturation and makes the inductance Lq in the q axis smaller than the
inductance Ld in the d axis. FIG. 12 is a graph showing a variation in
magnetic flux density B plotted against an external magnetic field H
including electric currents. In the graph of FIG. 12, the slope of the
tangent at each point of a curve Cq corresponding to the q axis and the
slope of the tangent at each point of a curve Cd corresponding to the d
axis respectively represent the inductances Lq and Ld. In the initial
state under the high-torque condition, Cq exists in a nonlinear area B.
Superposition of a negative voltage upon the initial voltage in the
.delta. axis, which is estimated as the q axis by the control ECU 100,
relieves the magnetic saturation in the q axis and shifts the curve Cq to
a linear range A. This enables detection of the electrical angle.
The CPU 120 waits for elapse of the sampling time ts at step S415, and
detects the electric currents I.gamma.1 and I.delta.1 in the directions of
the .gamma. axis and the .delta. axis at step S420. Although the sampling
time ts in this routine is identical with the sampling time ts in the
electrical angle detection routine under the low-torque condition, they
may be different from each other.
The CPU 120 subsequently outputs a voltage .DELTA.V.delta. in the
.delta.-axis direction at step S425, waits for elapse of the sampling time
ts at step S430, detects the electric currents I.gamma.2 and I.delta.2 in
the directions of the .gamma. axis and the .delta. axis at step S435, and
calculates the variations in electric currents .DELTA.I.gamma. and
.DELTA.I.delta. from the observed electric currents at step S440.
Calculation of the variations in electric currents at step S440 follows
the processing at step S340 in the electrical angle detection routine
under the low-torque condition shown in the flowchart of FIG. 6.
As described in the electrical angle detection process under the low-torque
condition, only the ratio of the variations in electric currents
.DELTA.I.gamma. and .DELTA.I.delta. is used for detection of the
electrical angle. One possible modification accordingly omits the
processing of steps S425 through S435 from the routine of FIG. 9 and
calculates the ratio of the variations in electric currents
.DELTA.I.gamma. and .DELTA.I.delta. only from the initial electric
currents I.gamma.0 and I.delta.0 obtained at step S405 and the electric
currents I.gamma.1 and I.delta.0 obtained at step S420. In the electrical
angle detection process under the high-torque condition, while a positive
voltage is applied at step S425 and S430, magnetic saturation may occur
again in the q-axis direction, which causes the electric current in the
.delta.-axis direction to be varied in a nonlinear manner. In some cases,
it is preferable to omit the processing of steps S425 through S435, in
order to avoid this possibility.
The CPU 120 specifies a division where the angular error .DELTA..theta.
exists, based on the calculated variations in electric currents
.DELTA.I.gamma. and .DELTA.I.delta. at step S445. The concrete procedure
of specifying the division is different from that adopted in the
electrical angle detection routine under the low-torque condition and
described with the graph of FIG. 11. FIG. 11 shows the variations in
electric currents plotted against the angular error .DELTA..theta.
(=.theta.-.theta.c) between the electrical angle .theta.c estimated by the
CPU 120 and the true electrical angle .theta.. The variations in electric
currents .DELTA.I.gamma. and .DELTA.I.delta. are expressed respectively by
Equation (7)
.DELTA.I.gamma.=.DELTA.V.delta..multidot.t.multidot..DELTA.I.multidot.sin2
.DELTA..theta. and Equation (8)
.DELTA.I.delta.=.DELTA.V.delta..multidot.t.multidot..DELTA.I.multidot.(A.m
ultidot.cos2.DELTA..theta.) given above, where A=(1/Ld+1/Lq)/2 and
.DELTA.I=(1/Ld-1/Lq)/2. When
.DELTA.I.delta.A=.DELTA.V.delta..multidot.t.multidot.A-.DELTA.I.delta.,
.DELTA.I.delta.A is expressed as Equation (25) given below:
##EQU3##
The plots of FIG. 11 show the variations in electric currents
.DELTA.I.gamma. and .DELTA.I.delta.A.
The CPU 120 applies the voltage in the .delta.-axis direction, so that
.DELTA.I.gamma.=0 when the angular error .DELTA..theta.=0. As explained
with Equations (7) and (25), .DELTA.I.gamma. and .DELTA.I.delta.A
theoretically vary with variations in the sine function and the cosine
function according to the angular error .DELTA..theta..
The range of -180 degrees to 180 degrees where the angular error
.DELTA..theta. may exist is divided into sixteen as divisions 1 through 16
shown in FIG. 11. The division where the angular error .DELTA..theta.
exists is specified according to the positive and negative signs of
.DELTA.I.gamma.+.DELTA.I.delta.A and .DELTA.I.gamma.-.DELTA.I.delta.A as
follows:
Case 1: when .DELTA.I.gamma.+.DELTA.I.delta.A>0 and
.DELTA.I.gamma.-.DELTA.I.delta.A>0, possible divisions where the angular
error exists are divisions 2, 3, 10, and 11;
Case 2: when .DELTA.I.gamma.+.DELTA.I.delta.A>0 and
.DELTA.I.gamma.-.DELTA.I.delta.A<0, possible divisions where the angular
error exists are divisions 1, 8, 9, and 16;
Case 3: when .DELTA.I.gamma.+.DELTA.I.delta.A<0 and
.DELTA.I.gamma.-.DELTA.I.delta.A<0, possible divisions where the angular
error exists are divisions 6, 7, 14, and 15; and
Case 4: when .DELTA.I.gamma.+.DELTA.I.delta.A<0 and
.DELTA.I.gamma.-.DELTA.I.delta.A>0, possible divisions where the angular
error exists are divisions 4, 5, 12, and 13.
The CPU 120 subsequently calculates the angular error .DELTA..theta.
corresponding to the specified division at step S450. The angular error
.DELTA..theta. is calculated by approximate equations, which are valid in
the range of relatively small .DELTA..theta. and expressed as Equations
(26) through (33) given below corresponding to the respective cases 1
through 4:
Case 1:
.DELTA..theta.=.DELTA.I.gamma./(2.multidot..DELTA.I.delta.A)+.pi./4(26)
.DELTA..theta.=.DELTA.I.gamma./(2.multidot..DELTA.I.delta.A)+5.pi./4(27)
Case 2:
.DELTA..theta.=-.DELTA.I.delta.A/(2.multidot..DELTA.I.gamma.)(28)
.DELTA..theta.=-.DELTA.I.delta.A/(2.multidot..DELTA.I.gamma.)+.pi.(29)
Case 3:
.DELTA..theta.=.DELTA.I.gamma./(2.multidot..DELTA.I.delta.A)+3.pi./4(30)
.DELTA..theta.=.DELTA.I.gamma./(2.multidot..DELTA.I.delta.A)+7.pi./4(31)
Case 4:
.DELTA..theta.=-.DELTA.I.delta.A/(2.multidot..DELTA.I.gamma.)+.pi./2(32)
.DELTA..theta.=-.DELTA.I.delta.A/(2.multidot..DELTA.I.gamma.)+3.pi./2(33)
Like the electrical angle detection process under the low-torque condition,
there are two equations for calculating the electrical angle with respect
to each of the cases 1 through 4. The technique of this embodiment sets an
appropriate value to the cycle for executing the electrical angle
detection routine under the high-torque condition and determines the
electrical angle only with Equations (26), (28), (30), and (32). As
described previously, one possible application carries out determination
of the polarity, which enables the electrical angle to be determined
unequivocally in the range of -180 degrees to 180 degrees.
The CPU 120 subsequently corrects the estimated electrical angle .theta.c
with the calculated angular error .DELTA..theta. at step S455. The program
completes the electrical angle detection process under the high-torque
condition at step S400 and returns to the motor control routine under
low-speed operation shown in the flowchart of FIG. 5. The CPU 120 carries
out the motor currents control process based on the detected electrical
angle at step S500. The details of the motor currents control process have
been discussed previously.
As a matter of convenience, the motor currents control process and the
electrical angle detection process are collectively shown in one flowchart
and assumed to be carried out at an identical cycle. In the actual state,
however, the motor currents control process is executed more frequently
than the electrical angle detection process, in order to attain the smooth
rotation of the synchronous motor 40. In this embodiment, the frequency of
the motor currents control process is four times the frequency of the
electrical angle detection process. The motor currents control without the
electrical angle detection is based on the electrical angle, which is
determined by interpolating the observed variations of the electrical
angle. The method of interpolation is described with the drawing of FIG.
13.
The graph of FIG. 13 shows an increase in electrical angle with an elapse
of time when the synchronous motor 40 is at a low-speed rotation. The
electrical angle detection process is carried out at points m1 through m5,
which are shown by the closed circles and are arranged at time intervals
.DELTA.tm. The electrical angle detection process is not carried out but
only the motor currents control process is carried out at points n1
through n3, which are shown by the open circles and are arranged at time
intervals .DELTA.tn. In this embodiment, .DELTA.tm=4.times..DELTA.tn.
An electrical angle N1 at the point n1 should be determined to execute the
motor currents control at the point n1. The method of this embodiment
calculates the electrical angle N1 according to an equation of
N1=.DELTA.mav.times.tn+M4, where .DELTA.mav denotes a mean rate of change
of the electrical angle calculated from the data at the points m1 through
m4 in FIG. 13, .DELTA.tn denotes the time interval, and M4 denotes an
electrical angle at the point m4. In a similar manner, electrical angles
at the points n2 and n3 are calculated using 2.times..DELTA.tn and
3.times..DELTA.tn, instead of .DELTA.tn.
The mean rate of change of the electrical angle .DELTA.mav is the mean of a
rate of variation of the electrical angle .DELTA.m1 between the points m1
and m2, a rate of change of the electrical angle .DELTA.m2 between the
points m2 and m3, and a rate of change of the electrical angle .DELTA.m3
between the points m3 and m4. Namely
.DELTA.mav=(.DELTA.m1+.DELTA.m2+.DELTA.m3)/3. The rate of change of the
electrical angle is obtained by dividing a variation in electrical angle
in each division by the time interval .DELTA.tm, and corresponds to the
mean angular velocity of the synchronous motor 40 in the division. Such
interpolation enables the electrical angle to be estimated at the point
m5, which is the next timing of electrical angle detection. The electrical
angle thus estimated is .theta.c shown in FIG. 4.
The motor currents control carried out at the higher frequency than that of
the electrical angle detection enables the operation of the synchronous
motor 40 to be controlled smoothly although the electrical angles at the
points n1 through n3 include some errors. The number of points, for
example, m1, m2, . . . , used for calculating the interval of the motor
currents control and the mean rate of change of the electrical angle are
determined appropriately according to the accuracy of estimation of the
electrical angle required for the motor currents control and the
processing speed of the CPU 120.
The electrical angle detection apparatus and the motor control apparatus 10
described above can detect the electrical angle with a high accuracy and
appropriately control the synchronous motor 40 even under the condition of
a high torque command value while the motor 40 is in the state of
low-speed operation. There is a possibility of an instantaneous torque
decrease due to application of a negative voltage in the q-axis direction,
which is a main dominant factor of the torque of the motor 40 in the
electrical angle detection process under the high-torque condition (step
S400 in the flowchart of FIG. 5). The voltage is applied in the q-axis
direction, however, only when the input torque command value is greater
than the predetermined torque T1. This arrangement of the embodiment
effectively reduces such a torque variation to the minimum level.
The electrical angle detection process is completed within a very short
time period. One possible modification omits the comparison between the
input torque command value and the predetermined torque T1 (step S200 in
the flowchart of FIG. 5) and detects the electrical angle according to the
electrical angle detection routine under the high-torque condition (step
S400 in the flowchart of FIG. 5) irrespective of the magnitude of the
torque command value. Another possible modification carries out both the
electrical angle detection process under the low-torque condition and the
electrical angle detection process under the high-torque condition
irrespective of the magnitude of the torque command value, and selects the
appropriate one out of both the results of the operations, in order to
enable the observed electrical angle of the motor 40 to continuously vary.
This modified structure is effective for stably detecting the electrical
angle in the case where the input torque command value is dose to the
predetermined torque T1, that is, in the transient range between the
electrical angle detection process under the low-torque condition and the
electrical angle detection process under the high-torque condition shown
in the flowchart of FIG. 5. Both the electrical angle detection routines
may be carried out only in such a transient range.
As shown in the graph of FIG. 10, the electrical angle detection apparatus
of the embodiment first applies a negative voltage to the q axis to be
superposed upon the initial voltage and then applies and superposes a
positive voltage in the electrical angle detection process under the
high-torque condition. This arrangement enables the q-axis electric
current decreased by application of the negative voltage to be quickly
recovered to a predetermined level corresponding to the required torque,
thereby suppressing the effect of the torque variation in the process of
detecting the electrical angle. With a view to calculating the rate of
change of the electric current with a high accuracy, the positive voltage
applied at step S425 and the negative voltage applied at step S410 in the
flowchart of FIG. 9 have an identical absolute value and an identical time
period of voltage application. The absolute value and the time period of
voltage application may, however, be appropriately set for the positive
voltage, in order to interfere with the torque variation.
Another possible modification may vary either the applied voltage
.DELTA.V.delta. or the time period of voltage application according to the
torque command value in the electrical angle detection process under the
high-torque condition executed by the electrical angle detection
apparatus. In accordance with a concrete procedure of this modified
structure, a large value is set to the applied voltage .DELTA.V.delta.
when the torque command value significantly exceeds the predetermined
torque (a point c in the graph of FIG. 1 2). The applied voltage
.DELTA.V.delta. decreases with a decrease in torque command value (a point
b in the graph of FIG. 12).
FIGS. 14 through 16 show the relationships between the torque command value
and the applied voltage .DELTA.V.delta.. In the graph of FIG. 14, the
absolute value of the applied voltage linearly decreases with a decrease
in torque command value. In the graph of FIG. 15, the absolute value of
the applied voltage decreases curvilinearly with a decrease in torque
command value. In the graph of FIG. 16, the absolute value of the applied
voltage decreases stepwise with a decrease in torque command value. In any
case, either one of the absolute value of the applied voltage and the time
period of voltage application may be decreased, or alternatively both may
be decreased.
In the electrical angle detection apparatus and the motor control apparatus
10, at least one of the absolute value of the applied voltage and the time
period of voltage application is decreased with a decrease in torque
command value required for the motor 40. This structure enables the
inductance of the q axis under the high-torque condition to be shifted to
a linear range (the range A in the graph of FIG. 12) by application of a
minimum required voltage. This accordingly minimizes the torque variation
due to application of the negative voltage to the q axis.
4. Motor Control Routine under Low-Speed Operation in Second Embodiment
The following describes a second embodiment according to the present
invention. The electrical angle detection apparatus and the motor control
apparatus 10 of the second embodiment have the identical hardware
structure with that of the first embodiment. The general flow of the motor
control routine under low-speed operation in the second embodiment is also
similar to that in the first embodiment and follows the flowchart of FIG.
5. The only difference of the second embodiment from the first embodiment
is the electrical angle detection process under the high-torque condition
(step S400 in the flowchart of FIG. 5).
FIG. 17 is a flowchart showing an electrical angle detection routine under
the high-torque condition that is executed in the second embodiment. When
the program enters the electrical angle detection routine under the
high-torque condition, the CPU 120 detects an initial value I.delta.0 of
the electric current in the .delta.-axis direction at step S460. As
described later, the second embodiment detects the electrical angle only
with the electric current in the .delta.-axis direction, which corresponds
to the q axis, and accordingly does not require detection of the initial
value of the electric current in the .gamma.-axis direction.
The concrete procedure of detecting the electric current in the
.delta.-axis direction is similar to that of the first embodiment. The CPU
120 receives signals output from the electric current sensors 102, 103,
and 104, which measure the electric currents of the U, V, and W phases,
via the filters 106, 107, and 108, the ADCs 112, 113, and 114, and the
input port 116, and converts the input electric currents of the U, V, and
W phases into the electric current in the 8-axis direction based on the
arithmetic operations discussed in (2) Motor Currents Control Process.
Since the d axis and the q axis can be defined only after the
determination of the electrical angle of the synchronous motor 40 as shown
in FIG. 4, the CPU 120 estimates the .delta. axis based on an estimated
electrical angle .theta.c and determine the electric current in the
.delta.-axis direction. There is accordingly an angular error
.DELTA..theta. between the estimated electrical angle .theta.c and an
actual electrical angle .theta. as shown in FIG. 4.
The CPU 120 then applies a detection voltage .DELTA.V.delta. in the
.delta.-axis direction, which is specified based on the estimated
electrical angle .theta.c, at step S465. This is equivalent to
superposition of a positive voltage .DELTA.V.delta. upon the initial
voltage or addition of .DELTA.V.delta. to the initial voltage. While the
first embodiment applies a negative voltage to the .delta. axis to be
superposed upon the initial voltage, the second embodiment applies a
positive voltage to the .delta. axis. The arrangement of the second
embodiment may, however, be realized by application of a negative voltage
as described later.
The CPU 120 waits for elapse of the sampling time ts at step S470, detects
the electric current I.delta.1 in the direction of the .delta. axis at
step S475, and calculates a variation in electric current .DELTA.I.delta.,
which is a difference from the observed initial electric current I.delta.0
at step S480. Whereas the first embodiment carries out the processing that
eliminates the error regarding the variation in electric current due to a
dead time loss (for example, the processing of steps S425 through S440 in
the flowchart of FIG. 9), the second embodiment detects the electrical
angle with a table including such errors and thereby does not require the
processing to avoid the dead time loss. In the case where the table used
for detection of the electrical angle does not include the effects of the
dead time loss, the second embodiment also requires the correction
discussed in the first embodiment.
The CPU 120 subsequently determines coefficients k1 and k2 applied for
calculation of the electrical angle according to the torque command value
at step S485. These coefficients k1 and k2 represent the slope and the
intercept of an approximate plane curve, which approximates to the
relationship between the angular error of the electrical angle and the
variation in electric current .DELTA.I.delta.. The coefficients k1 and k2
are mapped to the torque command value and stored in the form of a table.
A concrete procedure of step S485 reads the coefficients k1 and k2
corresponding to the calculated variation in electric current
.DELTA.I.delta. from the table and carries out interpolation according to
the requirements, thereby determining the coefficients k1 and k2.
The graph of FIG. 18 shows the relationships between the angular error of
the electrical angle and the variation in electric current .DELTA.I.delta.
with respect to a variety of torque command values. Parameters i1, i2, . .
. represent the torque command values, and the torque command value
increases in this sequence of the parameters i1, i2, . . . The reason of
the presence of such relationships shown in FIG. 18 has been described
previously. The relationships vary with the initial voltage of the motor
40, the detection voltage to be superposed upon the initial voltage, and
the time and are determined experimentally. The graph of FIG. 18 shows the
observed electric currents including the errors due to the dead time loss
with respect to the applied voltage.
In the graph of FIG. 18, the curves of the variation in electric current
.DELTA.I.delta. having significant differences according to the torque
command value (i3 through i6) correspond to the high-torque condition. The
threshold value T1 used to determine whether or not the electrical angle
detection process under the high-torque condition is carried out in this
embodiment (see step S200 in the flowchart of FIG. 5) is accordingly
between the value i2 and the value i3. The threshold value may not
coincide with the threshold value T1 in the first embodiment.
As shown in the graph of FIG. 18, the variation in electric current may be
approximated by a plane curve in the range of the angular error from -20
degrees to 40 degrees. The coefficients k1 and k2 represent the slope and
the Y intercept of the approximate plane curve. In the case where the
angular error exceeds the above range, the variation in electric current
can not be approximated by a plane curve as clearly understood from the
graph of FIG. 18. The structure of the embodiment detects the electrical
angle with a high frequency that enables the angular error to be kept
within this range according to the revolving speed of the motor 40,
thereby assuring the sufficient accuracy by the technique of plane curve
approximation.
The CPU 120 calculates the angular error .DELTA..theta. from the
coefficients k1 and k2 thus determined at step S490 and corrects the
estimated electrical angle .theta.c with the calculated angular error
.DELTA..theta. at step S495. The concrete procedure of this embodiment
calculates the angular error .DELTA..theta. from the coefficients k1 and
k2 and the variation in electric current .DELTA.I.delta. according to he
equation of .DELTA..theta.=k1.multidot..DELTA.I.delta.+k2.
Like the first embodiment, the electrical angle detection apparatus and the
motor control apparatus 10 of the second embodiment can detect the
electrical angle with a high accuracy and appropriately control the
synchronous motor 40 even when a high torque is required while the motor
40 is in the state of low-speed operation. The second embodiment applies a
positive voltage in the q-axis direction, which affects the output torque,
to detect the electrical angle. This arrangement effectively prevents the
output torque from being lower than the required torque. The second
embodiment does not require the processing to cancel the errors due to the
dead time loss (for examples, the processing of steps S425 through S440 in
the flowchart of FIG. 9) in the process of detecting the variation in
electric current. The structure of the embodiment accordingly realizes the
higher-speed processing, compared with the electrical angle detection
apparatus of the first embodiment.
The second embodiment detects the electrical angle at frequent intervals
and prevents the angular error from being deviated from the range of -20
degrees to 40 degrees, in order to approximate the variation in electric
current by a plane curve as shown in FIG. 18 and thereby improve the
processing speed. One possible modification divides the graph of FIG. 18
into a plurality of divisions and adopts the technique of plane curve
approximation. This enables the electrical angle to be detected even out
of the range of the angular error. With a view to enhancing the accuracy
of detection of the electrical angle, the variations in electric current
may be approximated by curves or stored in the form of a table.
As clearly understood from FIG. 18, when the angular error is within the
range of approximately -90 degrees to -30 degrees, there is only a slight
variation in electric current according to the angular error. This does
not ensure the sufficient accuracy of detection. When an extremely large
error of the electrical angle is expected, for example, when the control
procedure starts controlling the three-phase synchronous motor 40 that is
at a stop, it is desirable that another technique of detecting the
electrical angle is applied in combination with the technique of the
embodiment, in order to restrict the range of the angular error. One
example of the technique of detecting the electrical angle applicable in
combination with the technique of the embodiment is disclosed in JAPANESE
PATENT LAID-OPEN GAZETTE No. 7-177788.
In the second embodiment described above, the relationship between the
angular error and the variation in electric current is stored in advance.
One possible application uses, instead of this relationship, the
relationship between the angular error and the required time period from
the time point at which application of the detection voltage starts to the
time point at which the variation in electric current reaches a
predetermined level. This structure effectively prevents the electric
current from significantly exceeding the rated level of the three-phase
synchronous motor 40.
In the second embodiment, a positive voltage is applied for detection of
the electrical angle. A negative voltage may, however, be applied in the
method of the second embodiment. For example, a negative voltage is
applied for detection of the electrical angle in the case where
superposition of a positive detection voltage upon the initial voltage
applied corresponding to the torque command value may cause the electric
current to significantly exceed the rated level of the three-phase
synchronous motor 40. In this case, the relationship corresponding to that
of FIG. 18 with respect to a negative applied voltage should be
experimentally determined in advance.
The present invention is not restricted to the above embodiments or their
modifications, but there may be many other modifications, changes, and
alterations without departing from the scope or spirit of the main
characteristics of the present invention.
It should be clearly understood that the above embodiments are only
illustrative and not restrictive in any sense. The scope and spirit of the
present invention are limited only by the terms of the appended claims.
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